Computer aided engineering (CAE) has been used for supporting engineers in many tasks. For example, in a structure or product design procedure, CAE analysis, in particular finite element analysis (FEA), has often been employed to evaluate responses (e.g., stresses, displacements, etc.) under various loading conditions (e.g., static or dynamic).
FEA is a computerized method widely used in industry to simulate (i.e., model and solve) engineering problems relating to complex products or systems (e.g., cars, airplanes, etc.) such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. The geometry is defined by elements and nodes. There are many types of elements, solid elements for volumes or continua, shell or plate elements for surfaces and beam or truss elements for one-dimensional structure objects. One of the most challenging simulations is related to contacts between two or more locations of the FEA model.
Simulating contacts are routinely used in impact events of two or more objects, for example, automobile crash, sheet metal forming, etc. To numerically simulate such event, prior art approaches have used a technique referred to as surface-to-surface contact because the majority of the finite element models comprise two-dimensional 3- or 4-node low order shell or solid elements with their outer surface represented by either triangles or quadrilaterals. In order to perform a surface-to-surface contact simulation, the user needs to specify which surfaces in a finite element analysis model are to be included. In certain circumstance, each contact surface may fold and contact itself during the impact event. To simplify user input, modern approach for such a situation (self contacts) is to include all surfaces in one single self-contact surface definition which, for example, is commonly performed in car crash simulations (i.e., designating the entire vehicle as one single self-contact surface).
For computation efficiency, the finite element analysis model comprises non-quadratic low-order finite elements (i.e., finite elements defined by corner nodes only, for example, 3-node triangular 101, 4-node quadrilateral 102, 4-node tetrahedral 103, 8-node hexahedral elements 104 shown in FIG. 1). With the advent of faster computer systems, some users are desirous of including quadratic finite elements (i.e., finite elements 202, 204, 205, 252, 254 defined by more than just corner nodes shown in FIGS. 2A and 2B) in the finite element model. However, prior approaches of defining contact surfaces cannot accommodate quadratic finite elements without a significant degradation in performance. Since contact treatment can be nearly as costly as processing the elements and nodes in a realistic numerical simulation, many man years have been expended to ensure that contact is as optimized as possible to reduce computer run times. Closed form solutions for finding contact points are used for the lower order segments and segments of the same type are processed together to increase efficiency. Accurate and robust closed form solutions for finding the contact point are not available for quadratic finite elements, which leads to an iterative solution for the contact point. Such iterative solutions are not robust insofar as the surfaces can become very distorted due to the severe loadings seen in impact simulations. The inclusion of both lower and higher order contact surface segments (i.e., linear and quadratic finite elements) within the same contact surface definition creates interactions between the different segment types that require special branching in the computer software that ultimately destroys computation efficiency. The branching requires checking, for example, 1) lower order 3- and 4-node segments in contact, 2) quadratic 6- and 8-node segments in contact, and 3) lower order and quadratic segments in contact.
Furthermore, an interface force database displays surface pressure and shear stress distributions throughout the contact surface. This database is written at time intervals defined by the user for post-processing in multiple software products that presently lack the facility of treating quadratic contact surfaces while rendering the data. Therefore, it is imperative to preserve the current database in its present form to enable visualization of the contact stress distributions.
It would, therefore, be desirable to have methods and systems for creating a contact surface definition involving a mixture of quadratic and lower order linear finite elements in a finite element model used in numerical simulations of an impact event.